The full list of type I superconformal algebras, which follows directly from Kac's classification [1]}, is
\(\mathfrak {sl}(2|\mathcal {N}),\quad \mathfrak {sl}(2|\mathcal {N}_1)\oplus \mathfrak {sl}(2|\mathcal {N}_2),\quad \mathfrak {psl}(2|2),\quad \mathfrak {osp}(2|4),\quad \mathfrak {sl}(4|\mathcal {N}),\quad \mathfrak {psl}(4|4) .\) 
